Optical frequency combs, which consist of precisely controlled spectral lines covering a wide range, have played a crucial role in enabling numerous scientific advancements. Beyond the conventional approach that relies on mode-locked lasers, microcombs generated from microresonators pumped at a single frequency have arguably given rise to a new field within cavity nonlinear photonics, which has led to a robust exchange of ideas and research between theoretical, experimental, and technological aspects. Microcombs are extremely attractive in applications requiring a compact footprint, low cost, good energy efficiency, large comb spacing, and access to nonconventional spectral regions. The recently arising microcombs based on fiber Fabry–Pérot microresonators provide unique opportunities for ultralow noise and high-dimensional nonlinear optics. In this review, we comprehensively examine the recent progress of fiber Kerr microcombs and discuss how various phenomena in fibers can be utilized to enhance the microcomb performances that benefit a plethora of applications.